Ratio word problems and proportions dealing with word problems.
If 48 marbles are to be divided between bill and carl in the ratio 3:5 how man y marbles will bill get?
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Another way to approach this question would be to consider how many equal parts are being distrubed. Looking at the ratio of 3:5 as "for every 3 marbles that Bill gets, Carl get 5," it is easier understand that the marbles will be split into 8 equal parts.
The total marbles: 48 ;
divided by the number of equal parts: 8
gives you 8 groups of 6 marble.
If Bill gets 3 of the groups (each having 6 marbles)
he has a total of 6*3 marbles or 18 marbles.
Bill gets 3/(3+5) of the total.
(3/8)48 = 18
Answer: Bill gets 18 marbles.
x=one unit of marbles...
the ratio is 3 to 5
Bill gets 3 marbles for every 8 there are
there are 48 marbles
(3x)/(5x) for some x simplifies to 3/5 and 3x+5x=48
3*6=18 and 5*6=30
18/30 obviously simplifies to 3/5
the ratio is # of Bill's marbles/# of Carl's marbles, so Bill gets 18 marbles
This is a good problem to use ratio/proportion but we have to make sure we use the correct ratio when solving. The ratio we are given is 3:5 but that is Bill:Carl. We are also given the total so our ratio should be set up as Bills Marbles:Total Marbles. That would be 3:8. We know that the total marbles is 48. The unknown is Bill's marbles (x).
So since the ratios have to be the same we know that x:48 = 3:8 or x/48 = 3/8.
Cross multiply 8x = 144.
Divide each side by 8. 8x/8 =144/8.
x = 18. Carl gets the other 30. Bill:Carl = 18:30 = 3:5.